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The Cardinalities of A+A and A-A

Published online by Cambridge University Press:  20 November 2018

Sherman K. Stein
Sherman K. Stein*
Affiliation:
University Of California, Davis, California
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H. T. Croft's Research Problems, 1967, contains the following problem due to J. H. Conway. "Let A = {a1, a2,…, aN} be a finite set of integers, and define

and

Prove that A—A always has more members than A+A, unless A is symmetric about 0."Marica in [1] showed that the conjecture is false for the set A = {1, 2, 3, 5, 8, 9, 13, 15, 16}. In this case A+A has 30 elements and A—A has 29 elements.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 343 - 345
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Marica, J., On a conjecture of Conway, Canad. Math. Bull. 12 (1969), 233–234.Google Scholar